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Problem 57 Hard Difficulty

A light ray enters a rectangular block of plastic at an angle $\theta_{1}=45.0^{\circ}$ and emerges at an angle $\theta_{2}=76.0^{\circ},$ as shown in Figure P 22.57 . (a) Determine the index of refraction of the plastic. (b) If the light ray enters the plastic at a point $L=50.0 \mathrm{cm}$ from the bottom edge, how long does it take the light ray to travel through the plastic?

Answer

a. $\text { The index of refraction of plastic is }$ n=1.20
b. $\text { The time taken for a light ray to travel through plastic is } 3.39 \mathrm{ns}$

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Top Physics 103 Educators
Christina K.

Rutgers, The State University of New Jersey

Andy C.

University of Michigan - Ann Arbor

Zachary M.

Hope College

Meghan M.

McMaster University

Video Transcript

let us say we have a block off a plastic here of lock off plastic and this is the horse gentle. This will be normal to the surface, like strikes this point here and then with threats, and it strikes the other part here it emerges out off the glass, the plastic and makes an angle office off. That too. This we call it. Said that three and this one. We call it that They want the distance from here to here. We call it X, and this distance is l. Um Here's the end. This is hair Here, here, we can use their smells. Oh, that is in one times a sign that our one is a court in two. Sign that too on one is the one degrees on this is make that one is making 45 degrees. So sign 45 visible to end times. Sign that the three. Um so this is a party. The reflection that the bottom surface will be from here. It's called a state of one. The reflection of the bottom, Sir, Face at the data too is equal to 76 degrees. Then we can write in times sign 90 minus stated. Three is equal to one time science. And before 76 fathers, then ah, sign end unsigned 90 minus state a tree. Is it called? One? Don't sign 76. This part comes holes angle three better three other. This is called the one time Signed 76. From here this will come down here and then this becomes a tank that the three visible sign 45 divided by sign 76 more physical to Europe on 7 to 86. Then from here we can find that the three that the three will be tainted worse, off 0.7 to 86 was User said that the three or 36.8 And from here we can find end with physical to sign 45 divided by a subsidiary Ellie for 33 which is 36.8 Excuse it. They're effective. Next for a for a plastic to be 1.2 Oh, any to be one point 204 Plastic plastic But be they lost you for a light lost t off light is given by in a plastic This is the lost your flight in a plastic is given by we is equal to the speed of light and evacuated by the refracting X speed off Lighting evacuees three times gentle our age, divided by refraction Index. Want to excuse us the velocity of light in the classics to be 2.5 dimes? Think our eight meter per second what we have. Ah, the left off the plastic law to be 15 20 meter, which is a good is important. Five meter and a sign They're the three Easy pool to LD Right my ex from here. Excellent equal to 0.5 Divided by sign thirties six 108 This Q's are so X is equal to zero point age for nine meters. Then we can find a time that light travels inside. The plastic is by dividing the distance X divided by velocity for a speed. So X ray have is there a 0.849 divided by speed off light in Castaic, which we found 2.5 times? This gives us time. The light spends in X distance to be 3.39 times through the power dental about minus line seconds. Wow,

Wesleyan University
Top Physics 103 Educators
Christina K.

Rutgers, The State University of New Jersey

Andy C.

University of Michigan - Ann Arbor

Zachary M.

Hope College

Meghan M.

McMaster University